Diffusion limited aggregation and iterated conformal maps

The creation of fractal clusters by diffusion limited aggregation (DLA) is studied by using iterated stochastic conformal maps following the method pr oposed recently by Hastings and Levitov. The object of interest is the func tion Phi((n)) which conformally maps the exterior of the unit circle to the exterior of an n-particle DLA. The map Phi((n)) is obtained from rr stocha stic iterations of a function phi that maps the unit circle to the unit cir cle with a bump. The scaling properties usually studied in the literature o n DLA appear in a new light using this language. The dimension of the clust er is determined by the linear coefficient in the Laurent expansion of Phi( (n)), which asymptotically becomes a deterministic function of n. We find n ew relationships between the generalized dimensions of the harmonic measure and the scaling behavior of the Laurent coefficients.